Hindu-Arabic (Indian) System of Numeration

Whenever you see a six-digit cheque amount, read India’s population, or hear about a winning lottery, you’re seeing the Hindu-Arabic (Indian) System in action. It helps us make sense of large numbers in daily life!

• 10 Digit: Uses symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

• Base-10 System: Each place’s value increases tenfold as you move left.

• Place Value: The value of each digit depends on its position (ones, tens, hundreds, etc.).

• Zero as Placeholder: Allows for representation of any number, large or small.

• Origin: Developed in India and spread by Arab scholars.

In the Indian System, also called the Hindu-Arabic System, to read and write large quantities with ease, the groups are made with certain periods, as shown below:

Reading and Writing Large Numbers Using the Hindu-Arabic System:

1. 7456123 = 74,56,123
                   = Seventy-four lakh fifty-six thousand one hundred twenty-three.
2. 82854137 = 8,28,54,137
                     = Eight crore twenty-eight lakh fifty-four thousand one hundred thirty-seven.
3. 61786425 = 6,17,86,425
                     = Six crore seventeen lakh eighty-six thousand four hundred twenty-five.
4. 82854137 = 8,28,54, 137
                     = Eight crore twenty-eight lakh fifty-four thousand one hundred thirty-seven.
5. 743813256 = 74,38,13,256
                       = Seventy-four crore thirty-eight lakh thirteen thousand two hundred fifty-six.

Note:

1. Don’t use plurals when writing numbers in words (e.g., write five thousand, not five thousands).

2. Don’t use “and” between tens and ones in number words (e.g., write five hundred ninety-three, not five hundred and ninety-three).

3. Don’t use commas when writing numerals like 2,468. Instead, write Two thousand four hundred sixty-eight.

1. A check for ₹23,45,678 is written as

• 23,45,678 (figures)
• Twenty-three lakh forty-five thousand six hundred seventy-eight (in words)

2. Population data: “1,38,00,00,000” is spoken as “one hundred thirty-eight crore.”

• Commas: Always write from the right: first three digits, then every two digits.
• No “and” in words. Don’t use “and” (e.g., NOT “two hundred and fifty”).
• No plurals: Use “lakh”, not “lakhs.”
• Commas only in figures, not in words.
• Zero is never at the start (e.g., “07,21,096” is just “7,21,096”).